Large Deviations for Extremes of U-processes

We prove a large deviations principle (LDP) for partial sums U-processes indexed by the half line. The LDP can be formulated on a suitable subset of the set of all absolutely continuous paths. We endow the space with a topology, which is stronger than the usual topology of uniform convergence on compact intervals. An LDP for the maximum of the sample path of the U-processes is obtained as a particular application.